Advances in information technology have led to extremely large datasets that are often kept in different storage centers. Existing statistical methods must be adapted to overcome the resulting computational obstacles while retaining statistical validity and efficiency. Split-and-conquer approaches have been applied in many areas, including quantile processes, regression analysis, principal eigenspaces, and exponential families. We study split-and-conquer approaches for the distributed learning of finite Gaussian mixtures. We recommend a reduction strategy and develop an effective MM algorithm. The new estimator is shown to be consistent and retains root-n consistency under some general conditions. Experiments based on simulated and real-world data show that the proposed split-and-conquer approach has comparable statistical performance with the global estimator based on the full dataset, if the latter is feasible. It can even slightly outperform the global estimator if the model assumption does not match the real-world data. It also has better statistical and computational performance than some existing methods.
翻译:信息技术的进步已导致大量数据集,这些数据集往往保存在不同储存中心; 现有的统计方法必须加以调整,以克服由此造成的计算障碍,同时保持统计有效性和效率; 在许多领域,包括四分法进程、回归分析、主要电子元空间和指数式组别,应用了分解法和分解法,我们研究了有限高斯混合物分布式学习的分解法,我们建议减少战略并开发有效的MMM算法。 新的估计算法显示,在一般条件下,新的估计算法是一致的,并保持了根与根的一致性。 以模拟和现实世界数据为基础的实验显示,如果完全数据集可行,拟议的分解法方法与全球估计法具有可比的统计性能。 如果模型假设与真实世界数据不匹配,它甚至能略微超过全球估计法。 它还比某些现有方法在统计和计算上更好。